J. Chem. Eng. Data 1997, 42, 1191-1194
1191
Isobaric Vapor-Liquid Equilibria in the Systems Methyl 1,1-Dimethylethyl Ether + Octane and Heptane + Octane Jaime Wisniak,* Gabriela Embon, and Ran Shafir Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel 84105
Hugo Segura and Ricardo Reich Department of Chemical Engineering, Universidad de Concepcio´n, Concepcio´n, Chile
Vapor-liquid equilibrium at 94 kPa has been determined for the binary systems methyl 1,1-dimethylethyl ether (MTBE) + octane and heptane + octane. Both binary systems deviate slightly from ideal behavior, and neither system presents an azeotrope. The system MTBE + octane behaves like a regular solution. The activity coefficients and boiling points of both binary systems were well correlated with its composition by the Redlich-Kister, Wohl, Wilson, UNIQUAC, NRTL, and Wisniak-Tamir equations.
Use of oxygenated fuels in winter has become compulsory in the United States and other countries in the world. Since 1990 reformulated gasolines must contain at least 2% mass oxygen and a Reid vapor pressure below 59.3 kPa. In most cases the required oxygen is provided by alcohols such as methanol and ethanol or ethers such as methyl tert-butyl ether (MTBE), and ethyl tert-butyl ether (ETBE). MTBE is the primary oxygenated compound being used to reformulate gasolines to improve their octane rating and pollution-reducing capability. Phase equilibrium data of oxygenated mixtures are important for predicting the vapor phase composition that would be in equilibrium with hydrocarbon mixtures. Vapor-liquid equilibria for the system heptane + octane has been measured by Leslie and Carr (1925) at (12.3, 19.9, 31.1, 47.3, 70.1, and 101.3) kPa, by Beatty and Calingaert (1934) at 370.35 K, by Duty and Mayberry (1966) at (327.85, 337.15, 352.25, and 370.15) K, by Han et al. (1993), at (293.5, 312.75, and 328.15) K, by Kudryatseva et al. (1971) at 328.15 K, and by Zielkiewicz (1992) at 313.15 K. Hutchings and Van Hook (1985) determined the values of the excess Gibbs molar energy of the binary system at 323.15 K, and Golik and Baranovskii (1961) determined the enthalpies of vaporization of the same as a function of the composition of the system. The isobaric data reported by Leslie and Carr (1925) were obtained in order to build the Du¨hring graph of the system. The data reported are the boiling point of solutions at rounded values of the liquid composition (every 10 mol %), no indication is given regarding the thermodynamic consistency of the same. According to Zielkiewicz (1992) at 313.15 K the system heptane + octane presents small positive deviations from ideality and may be considered a regular solution. The same behavior has been reported by Han et al. (1993) at four temperature levels. No isothermal or isobaric vapor-liquid equilibria data are available for the system MTBE + octane. The present work was undertaken to measure vapor-liquid equilibria (VLE) data for the title systems for which isobaric data are either not very accurate or unavailable. Experimental Section Purity of Materials. Methyl 1,1-dimethylethyl ether (99.93 mass %), heptane (99.57 mass %), and octane (99.80 * To whom correspondence should be addressed. Email: wisniak@ bgumail.bgu.ac.il.
S0021-9568(97)00126-X CCC: $14.00
Table 1. Mole Percent GLC Purities (mass %), Refractive Index nD at the Na D Line, and Normal Boiling Points T of Pure Components component (purity/mass %)
nD (298.15 K)
T/K
methyl 1,1-dimethylethyl ether (99.93)
1.3661a 1.3663b
heptane (99.57)
1.3851a 1.38511d 1.3948a 1.3952f
328.3a 327.85b 328.31c 371.5a 371.553e 398.5a 398.83g
octane (99.80)
a Measured. b TRC a-6040, 1963. c Zykmundova et al. (1990). TRC fa-1460, 1991. e TRC k-1460, 1991. f TRC fa-1490, 1990. g TRC k-1490, 1990. d
mass %) were purchased from Aldrich. The reagents were used without further purification after gas chromatography failed to show any significant impurities. The properties and purity (as determined by GLC) of the pure components appear in Table 1. Apparatus and Procedure. An all glass vapor-liquidequilibrium apparatus model 602, manufactured by Fischer Labor-und Verfahrenstechnik (Germany), was used in the equilibrium determinations. In this circulation method apparatus, a volume of about 100 mL of the solution is heated to its boiling point by a 250 W immersion heater (Cottrell pump). The vapor-liquid mixture flows through an extended contact line that guarantees an intense phase exchange and then enters a separation chamber whose construction prevents an entrainment of liquid particles into the vapor phase. The separated gas and liquid phases are condensed and returned to a mixing chamber, where they are stirred by a magnetic stirrer, and returned again to the immersion heater. Temperature control is achieved by a 5 mm diameter Pt-100 temperature sensor, with an accuracy of (0.1 K. The total pressure of the system is controlled by a vacuum pump capable to work at pressures down to 0.25 kPa. The pressure is measured by a Vac Probs with an accuracy of (0.07 kPa. On the average the system reaches equilibrium conditions after 0.5-1 h of operation. Samples, taken by syringing out 0.7 µL after the system had achieved equilibrium, were analyzed by gas chromatography on a Gow-Mac series 550P apparatus equipped with a thermal conductivity detector and a Spectra Physics Model SP 4290 electronic integrator. The column was 3 m long and 0.2 cm in diameter, packed with © 1997 American Chemical Society
1192 Journal of Chemical and Engineering Data, Vol. 42, No. 6, 1997 Table 2. Experimental Vapor-Liquid Equilibrium Data for Methyl 1,1-Dimethylethyl Ether (1) + Octane (3) at 94 KPa T/K
x1
y1
γ1
γ3
395.95 387.65 385.25 384.65 381.25 379.15 375.85 373.05 368.75 364.85 354.05 352.35 350.85 348.05 346.75 344.35 342.05 340.75 332.45 329.35 325.75
0 0.044 0.060 0.064 0.089 0.104 0.129 0.154 0.188 0.226 0.353 0.374 0.403 0.442 0.457 0.504 0.549 0.579 0.782 0.883 1
0 0.243 0.312 0.318 0.407 0.443 0.513 0.566 0.638 0.693 0.820 0.836 0.850 0.878 0.888 0.906 0.922 0.931 0.972 0.987 1
1.139 1.117 1.088 1.071 1.049 1.047 1.029 1.046 1.035 1.024 1.029 1.010 1.024 1.037 1.026 1.023 1.015 1.003 0.992
0.994 0.985 0.997 0.984 1.000 0.995 0.996 0.993 1.004 1.022 1.022 1.037 1.002 0.993 0.999 0.996 0.994 1.099 1.077
-B11/(cm3 -B33/(cm3 -B13/(cm3 mol-1) mol-1) mol-1) 741 752 755 772 783 800 814 838 860 927 938 948 967 976 994 1010 1020 1086 1112
1872 1904 1912 1958 1987 2035 2076 2144 2208 2402 2436 2466 2523 2551 2603 2655 2685 2892 2976
1185 1204 1209 1237 1254 1282 1307 1347 1384 1497 1516 1533 1566 1582 1612 1641 1658 1773 1820
Figure 1. Boiling temperature diagram for the system methyl 1,1-dimethylethyl ether (1) + octane (3) at 94 kPa (s).
Table 3. Experimental Vapor-Liquid Equilibrium Data for Heptane (2) + Octane (3) at 94 KPa T/K
x2
y2
γ2
γ3
395.95 394.45 394.05 393.65 393.25 393.05 391.25 389.65 388.65 386.35 384.95 382.25 381.65 379.65 376.05 374.95 373.85 373.35 371.95 370.65 369.55 368.55
0 0.033 0.040 0.061 0.070 0.071 0.118 0.167 0.200 0.274 0.328 0.401 0.443 0.502 0.639 0.712 0.756 0.784 0.841 0.906 0.962 1
0 0.072 0.084 0.125 0.140 0.142 0.221 0.293 0.339 0.444 0.503 0.585 0.626 0.685 0.795 0.841 0.869 0.885 0.918 0.953 0.982 1
1.116 1.112 1.086 1.074 1.076 1.044 1.020 1.009 1.022 1.001 1.021 1.004 1.021 1.025 1.002 1.005 1.000 1.006 1.005 1.005
1.005 1.009 0.996 0.999 1.004 1.009 1.013 1.015 1.003 1.009 1.021 1.008 1.008 1.008 1.016 1.021 1.031 1.040 1.045 1.043
-B22/(cm3 -B33/(cm3 -B23/(cm3 mol-1) mol-1) mol-1) 1313 1317 1320 1323 1325 1341 1355 1363 1384 1397 1422 1428 1447 1483 1494 1505 1511 1525 1539 1551
1788 1793 1798 1802 1805 1827 1847 1860 1889 1908 1944 1952 1980 2032 2048 2064 2072 2093 2113 2131
1532 1536 1540 1544 1546 1564 1581 1592 1616 1632 1662 1669 1692 1735 1748 1762 1768 1786 1803 1817
SE-30. Injector and detector temperatures for both binaries were 493.15 and 543.15 K, respectively, and column temperatures were 399.25 K for the system methyl 1,1dimethylethyl ether (MTBE) + octane and 393.15 K for the system heptane + octane. Very good separation was achieved under these conditions, and calibration analyses were carried out to convert the peak ratio to the mass composition of the sample. The pertinent polynomial fits had a correlation coefficient R2 better than 0.99. Concentration measurements were accurate to better than (0.005 mole fraction. Results The temperature T and liquid-phase xi and vapor-phase yi mole fraction measurements at P ) 94 kPa are reported in Tables 2 and 3 and Figures 1 and 2, together with the activity coefficients γi that were calculated from the following equation (Van Ness and Abbott, 1982)
ln γi ) ln
yiP + xiP0i
(Bii - VLi )(P - P0i ) δijP + y2j RT RT
(1)
Figure 2. Boiling temperature diagram for the system heptane (2) + octane (3); this work at 94 kPa (s), data of Leslie and Carr at 101.3 kPa (0). Table 4. Antoine Coefficients, Eq 3 compound
Ai
Bi
Ci
methyl 1,1-dimethylethyl ethera heptaneb octanea
5.860 78 6.020 23 6.051 41
1032.988 1263.909 1354.107
59.876 56.718 63.888
a
Reich (1996). b TRC k-1460, 1991.
where T and P are the boiling point and the total pressure, VLi is the molar liquid volume of component i, Bii and Bjj are the second virial coefficients of the pure gases, Bij the cross second virial coefficient, and
δij ) 2Bij - Bjj - Bii
(2)
The standard state for calculation of activity coefficients is the pure component at the pressure and temperature of the solution. Equation 1 is valid at low and moderate pressures when the virial equation of state truncated after the second coefficient is adequate to describe the vapor phase of the pure components and their mixtures, and liquid volumes of the pure components are incompressible over the pressure range under consideration. The pure component vapor pressures P0i were calculated according to the Antoine equation
log(P0i /kPa) ) Ai -
Bi (T/K) - Ci
(3)
Journal of Chemical and Engineering Data, Vol. 42, No. 6, 1997 1193 Table 5. Parameters and Deviations between Experimental and Calculated Values for GE-Different Models A. Redlich-Kister, Eq 4 system
B
C
methyl 1,1-dimethylethyl ether (1) + octane (3)
0.0425 0.0425 0.0181
-0.0001 -0.0089
heptane (2) + octane (3)
B. Other model Wohl Wilson NRTL UNIQUAC
D
max dev %a
avg dev %b
rmsdc
0.0235
4.6 4.6 2.3
2.6 2.6 1.8
0.007 0.007 0.003
Modelsd
system
A12
A21
q1/q2
1+3 2+3 1+3 2+3 1+3 2+3 1+3 2+3
0.1244 0.1494 -35.67f -40.51 31.75f 51.64 67.64f 34.59
0.0417 0.0248 543.3f 391.7 29.85f -1.437 20.04f 14.31
3.7145 3.6681
δ(y)e
R
0.017 0.006 0.018 0.009 0.018 0.007 0.018 0.007
0.308 0.537
a Maximum deviation %. b Average deviation %. c Root-mean-square deviation. (N ) number of data points). f J/mol.
d
All equations in ln γi form. e δ(y) ) ∑|yexptl - ycalcd|/N
Table 6. Coefficients in Correlation of Boiling Points, Eq 6, Average % Deviation, and Root-Mean-Square Deviations in Temperature, rmsd (T/K) system
C0
C1
C2
C3
max dev %a
avg dev %b
rmsdc
methyl 1,1-dimethylethyl ether (1) + octane (3) heptane (2) + octane (3)
-65.082 60 -9.535 48
21.854 33 -0.222 96
-13.396 09 0.510 07
28.421 98 9.833 63
0.8 0.4
0.3 0.1
0.07 0.04
a
Maximum deviation %/K. b Average deviation %/K. c Root-mean-square deviation/K.
where the Antoine constants Ai, Bi, and Ci are reported in Table 4. The molar virial coefficients Bii and Bij were estimated by the method of O’Connell and Prausnitz (1967) using the molecular parameters suggested by the authors and assuming the association parameter η to be zero. Critical properties of MTBE were taken from a publication by Ambrose and Broderick (1974). The last two terms in eq 1, particularly the second one that expresses the correction due to the nonideal behavior of the vapor phase, contributed between 5 and 10% to the activity coefficients of both binary systems; in general, their influence was important only at very dilute concentrations. The calculated activity coefficients are reported in Tables 2 and 3 and are estimated accurate to within (2%. The results reported in these tables indicate that both binary systems deviate slightly from ideal behavior. For the sake of comparison, the vapor-liquid data reported by Leslie and Carr (1925) for the system heptane + octane at 101.3 kPa are also included in Figure 2. Inspection of Table 2 shows that the large difference in boiling point temperatures between MTBE and octane reflects a vapor phase very rich in MTBE; the relative volatility R ) (y1/x1)/(y2/x2) is 6.8 at x1 ) 0.1 and 10.1 at x1 ) 0.88. The vapor-liquid equilibria data reported in Tables 2 and 3 were found to be thermodynamically consistent by the L-W point-to point and area method of Wisniak (1993), except at the dilute ends, and the point-to-point method of Van Ness et al. (1973) as modified by Fredenslund et al. (1977). For both binaries, the residuals of the Fredenslund test were randomly distributed, as measured by the Durbin-Watson statistic. The activity coefficients of both binary systems were correlated well with the RedlichKister, Wohl, Wilson, NRTL, and UNIQUAC equations (Walas, 1985). The following expression was used for the Redlich-Kister (1948) expansion
Kister model gives a good representation of the data for both systems and that the behavior of the system MTBE + heptane approximates that of a regular solution. The parameters of the Wohl, Wilson, NRTL and UNIQUAC equations were obtained by minimizing the following objective function (OF)
log(γ1/γ2) ) B(x2 - x1) + C(6x1x2 - 1) + D(x2 - x1)(8x1x2 - 1) (4)
Ambrose, D.; Broderick, B. E. The Critical Temperature and Pressure of Thirty Organic Compounds. J. Appl. Chem. Biotechnol. 1974, 24, 359-372. Beatty, H. A.; Calingaert, G. Vapor-Liquid Equilibrium of Hydrocarbon Mixtures. Ind. Eng. Chem. 1934, 26, 504-508. Duty, R. C.; Mayberry, W. R. Vapor Pressure and Boiling Points of Hydrocarbon Solutions [determined] by Gas-Liquid Chromatography. J. Gas Chromatogr. 1966, 4, 115-120.
The values of the constants B, C, and D were determined by multilinear regression and appear in Table 5 together with the pertinent statistics. It is seen that the Redlich-
N
OF )
∑ i)1
(
) (
exptl calcd γ1,i - γ1,i
2
+
exptl γ1,i
)
exptl calcd γ2,i - γ2,i exptl γ2,i
2
(5)
and are reported in Table 5, together with the relative deviation of the vapor composition. Inspection of the results given in Table 5 shows that although the four models fitted both binary systems well the fit for the system heptane + octane was much better than that for the system MTBE + octane, probably because of the smaller difference between the boiling points of the pure components. The capability of predicting the vapor phase composition has been used as the ranking factor. The boiling points of the two binaries were correlated by the equation proposed by Wisniak and Tamir (1976): m
T/K ) x1T01 + x2T20 + x1x2
∑C
k
(x1 - x2)k
(6)
k)1
In this equation T0i /K is the boiling point of the pure component i at the operating pressure and m is the number of terms in the series expansion of (x1 - x2). The various constants of eq 6 are reported in Table 6, which also contains information indicating the degree of goodness of the correlation. Literature Cited
1194 Journal of Chemical and Engineering Data, Vol. 42, No. 6, 1997 Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC; Elsevier: Amsterdam, 1977. Golik, A. Z.; Baranovskii, V. E. Heats of Vaporization, Composition of the Vapors and Surface Tensions, of Solutions of Paraffins and Alcohols. Ukr. Khim. Zh. 1961, 27, 574-744. Han, B.; Yan, H.; Hu, R. Vapor Pressure of n-Heptane - n-Octane and n-Octane - Isooctane Binary Mixtures. Wuli Huaxue Xuebao, 1993, 9, 421-423. Hutchings, R. S.; Van Hook, A. Excess Molar Gibbs Free Energies of Pairs of n-Alkanes, the Two n-Alkanes Differing by One or Two Carbon Atoms. J. Chem. Thermodyn. 1985, 17, 531-538. Kudryatseva, L. S.; Viit, K.; Eisen, O. Vapor-Liquid Equilibrium in 1-Heptene-Heptane, 1-Heptene-Octane, Heptane-Octane, BenzeneThiophene, Benzene-Heptane, and Thiophene-Heptane at 55 °C. Eesti NSV Tead. Akad. Toim., Keem. Geol. 1971, 20, 292. Leslie, E. H.; Carr, A. R. Vapor Pressure of Organic Solutions and Application of Du¨hring’s Rule to Calculation of Equilibrium Diagrams. Ind. Eng. Chem. 1925, 17, 810-817. O’Connell, J. P.; Prausnitz, J. M. Empirical Correlations of Second Virial Coefficients for Vapor-Liquid Equilibrium Calculations. Ind. Eng. Chem. Process Des. Dev. 1967, 6, 245-250. Redlich, O; Kister, A. T. Algebraic Representation of Thermodynamic Properties and the Classification of Solutions. Ind. Eng. Chem. 1948, 40, 345-348. Reich, R. Personal communication, 1996. TRC-Thermodynamic Tables-Hydrocarbons; Thermodynamics Research Center, The Texas A&M University System: College Station, TX, extant 1996; fa-1490, 1990; fa-1460, 1991; k-1490, 1990; k-1460, 1991.
TRC-Thermodynamic Tables-Non-Hydrocarbons; Thermodynamics Research Center, The Texas A&M University System: College Station, TX, extant 1996; a-6040, 1963. Van Ness, H. C.; Abbott, M. M. Classical Thermodynamics of Nonelectrolyte Solutions; McGraw-Hill Book Co.: New York, 1982. Van Ness, H. C.; Byer, S. M.; Gibbs, R. E. Vapor-Liquid Equilibrium: Part I. An Appraisal of Data Reduction Methods. AIChE J. 1973, 19, 238. Walas, S. M. Phase Equilibria in Chemical Engineering; Butterworth Publishers: Boston, MA, 1985. Wisniak, J. A New Test for the Thermodynamic Consistency of VaporLiquid Equilibrium. Ind. Eng. Chem. Res. 1993, 32, 1531-1533. Wisniak, J.; Tamir, A. Correlation of the Boiling Point of Mixtures. Chem. Eng. Sci. 1976, 31, 631-635. Zielkiewicz, J. (Vapour-Liquid) Equilibrium in (Propan-1-ol + Heptane + Octane) at the Temperature 313.15 K. J. Chem. Thermodyn. 1992, 24, 455-462. Zykmundova, D.; Matous, J.; Novak, J. O.; Kubicek, V.; Pick, J. LiquidLiquid and Vapour-Liquid Equilibria in the System Methyl tertButyl Ether + Tetrahydrofuran + Water. Fluid Phase Equilib. 1990, 54, 93-110. Received for review May 16, 1997. Accepted July 28, 1997. This work was partially financed by FONDECYT, Chile, Project No. 1960583.X
JE970126K X
Abstract published in Advance ACS Abstracts, September 15, 1997.
